Most of the trade deadline attention has been on the Chicago Cubs' Matt Garza, but it may be shifting to a pitcher for Chicago's other team.

Jake Peavy of the White Sox is off the disabled list, and several teams in need of pitching help could be eyeing the veteran righthander. The Boston Red Sox, St. Louis Cardinals, New York Yankees and Baltimore Orioles all had scouts in Chicago Saturday for Peavy's first start since returning from the DL, FOXSports.com's Ken Rosenthal reports.

But Rosenthal points out it's not clear if all those teams are interested in the 32-year-old Peavy, who missed a month and a half with a fractured rib. The White Sox have other players on the trade market, including outfielder Alex Rios.

Peavy picked up a win while allowing four runs (two earned), seven hits and no walks and striking out three in six innings vs. the Atlanta Braves. Overall, he is 7-4 with a 4.19 ERA and 60 strikeouts in 12 starts this season.

Garza, 29, has put up better numbers this season, but several general managers and assistant general managers tell CBSSports.com's Jon Heyman they would favor trading for Peavy, who is a three-time All-Star with a Cy Young and two ERA titles on his resume.

"Peavy has been better than Garza except for lately and he has done it in a hitter's park in the American League,'' one NL GM said. "Garza's better for 2013, but I think Peavy has more overall value. Peavy was really good early until he got hurt.''

Also working in Peavy's favor: He is under contract through the end of the 2014 season. Garza can become a free agent after this season.

For their part, the White Sox are far out of contention and would love to dump Peavy's large contract (he is owed $14.5 million next season) while picking up some prospects.